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EE143 – Ali Javey
Section 12: Intro to Devices
Extensive reading materials on reserve, includingRobert F. Pierret, Semiconductor Device Fundamentals
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EE143 – Ali Javey
Bond Model of Electrons and Holes Silicon crystal in
a two-dimensionalrepresentation.
S i S i S i
S i S i S i
S i S i S i
Si Si Si
Si Si Si
Si Si Si
Si Si Si
Si Si Si
Si Si Si
When an electron breaks loose and becomes a conduction electron, a hole is also created.
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EE143 – Ali Javey
Semiconductors, Insulators, and Conductors
• Totally filled bands and totally empty bands do not allow current flow. (Just as there is no motion of liquid in a totally filled or totally empty bottle.)
• Metal conduction band is half-filled.• Semiconductors have lower EG’s than
insulators and can be doped
E c
Ev
Eg =1.1 eV
E c
E g = 9 eV empty
Si, Semiconductor SiO2
, insulator Conductor
E cfilled
Top of conduction band
E v
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EE143 – Ali Javey
-
+ Top of valence band
Bottom of conduction band
electron
hole
Energy gap=1.12 eV
n (electron conc)= p (hole conc) = ni
Intrinsic Carriers
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EE143 – Ali Javey
Dopants in Silicon
Si Si Si
Si Si
Si Si Si
Si Si Si
Si Si
Si Si Si
As B
As, a Group V element, introduces conduction electrons and creates N-type silicon,B, a Group III element, introduces holes and creates P-type silicon,
and is called an acceptor.
and is called a donor.
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EE143 – Ali Javey
Ionized
Donor
IonizedAcceptor
Immobile Chargesthey DO NOTcontribute to current flow with electric field is applied. However, they affect the local electric field
Hole
Electron
Mobile Charge Carriers they contribute to current flow with electric field is applied.
Types of charges in semiconductors
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EE143 – Ali Javey
Fermi Function–The Probability of an Energy State Being Occupied by an Electron
f(E)
0.5 1
Ef
Ef – kT
Ef – 2kT
Ef – 3kT
Ef + kT
EfEf + 2kT
Ef + 3kT
E
kTEE feEf /)(1
1)( Ef is called the Fermi energy or
the Fermi level.
kTEE feEf )( kTEE f
kTEE feEf 1)( kTEE f
Boltzmann approximation:
kTEE feEf )(
kTEE feEf 1)(
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EE143 – Ali Javey
Electron and Hole Concentrations
Remember: the closer Ef moves up to Ec, the larger n is; the closer Ef moves down to Ev , the larger p is.
For Si, Nc = 2.81019cm-3 and Nv = 1.041019 cm-3 .
kTEEc
CFeNn /)(
kTEEv
FVeNp /)(
Nc is called the effectivedensity of states.
Nv is called the effectivedensity of states of the valence band.
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EE143 – Ali Javey
Shifting the Fermi Level
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EE143 – Ali Javey
n: electron concentration (cm-3)
p : hole concentration (cm-3)
ND: donor concentration (cm-3)
NA: acceptor concentration (cm-3)
1) Charge neutrality condition: ND + p = NA + n
2) Law of Mass Action : n p = ni2
Assume completely ionized to form ND
+ and NA
-
Quantitative Relationships
What happens when one doping
species dominates?
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EE143 – Ali Javey
I. (i.e., N-type)
If ,
II. (i.e., P-type)
If ,
ad NNn
nnp i2
iad nNN
ad NN dNn di Nnp 2 and
ida nNN da NNp pnn i
2
da NN aNp ai Nnn 2 and
General Effects of Doping on n and p
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EE143 – Ali Javey
• When an electric field is applied to a semiconductor, mobile carriers will be accelerated by the electrostatic force. This force superimposes on the random thermal motion of carriers:
E.g. Electrons drift in the direction opposite to the E-field
Current flows
Average drift velocity = | v | = ECarrier mobility
12
3
45
electron
E
123
4
5
electron
E =0
Carrier Drift
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EE143 – Ali Javey
• Mobile carriers are always in random thermal motion. If no electric field is applied, the average current in any direction is zero.
• Mobility is reduced by
1) collisions with the vibrating atoms
“phonon scattering”
2) deflection by ionized impurity atoms “Coulombic scattering”
-
Si
-
As+
-B-
-
Carrier Mobility
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EE143 – Ali Javey
1E14 1E15 1E16 1E17 1E18 1E19 1E20
0
200
400
600
800
1000
1200
1400
1600
Holes
Electrons
Mo
bili
ty (
cm2 V
-1 s
-1)
Total Impurity Concenration (atoms cm-3)Na + Nd (cm-3)
impurityphonon
impurityphonon
111
111
Total Mobility
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EE143 – Ali Javey
Jp,drift = qpv = qppE
Jn,drift = –qnv = qnnE
Jdrift = Jn,drift + Jp,drift = E =(qnn+qpp)E
conductivity of a semiconductor is = qnn + qpp
Resistivity, = 1/
Conductivity and Resistivity
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EE143 – Ali Javey
N-type
P-type
= 1/
DOPA
NT D
ENSI
TY c
m-
3
RESISTIVITY
( cm)
Relationship between Resistivity and Dopant Density
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EE143 – Ali Javey
• Rs value for a given conductive layer (e.g. doped Si, metals) in IC or MEMS technology is used– for design and layout of resistors
– for estimating values of parasitic resistance in a device or circuit
W
LR
Wt
LR s
tRs
Rs is the resistance when W = L (in ohms/square)
if is independent of depth x
V
+_
L
tW
I
Material with resistivity
V
+_
L
tW
I
Material with resistivity
V
+_
L
tW
I
Material with resistivity
Sheet Resistance
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EE143 – Ali Javey
Particles diffuse from higher concentration to lower concentration locations.
Diffusion Current
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EE143 – Ali Javey
dx
dnqDJ ndiffusionn ,
dx
dpqDJ pdiffusionp ,
D is called the diffusion constant. Signs explained:
n p
x x
Diffusion Current
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EE143 – Ali Javey
Generation/Recombination Processes
Recombination continues until excess carriers = 0.Time constant of decay is called recombination lifetime
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EE143 – Ali Javey
Continuity Equations• Combining all the carrier actions:
• Now, by the definition of current, we know:
• Since a change in carrier concentration must occur from a net current
• Therefore, we can compactly write the continuity equation as:
otherstn
GthermalRtn
difftn
drifttn
tn
NqzJ
y
J
xJ
qdifftn
drifttn JNzNyNx
11 )(
othertp
GthermalRtp
Pqtp
othertn
GthermalRtn
Nqtn
J
J
1
1
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EE143 – Ali Javey
A PN junction is present in almost every semiconductor device.
N-type
P-type
Donors
V
I
Reverse bias Forward bias
N P
V
I
diodesymbol
– +
PN Junctions
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EE143 – Ali Javey
N-region P-region(a)
(b)
(c)
(d)
Depletionlayer
Neutral P-region
NeutralN-region
Ef
n 0 and p 0in the depletion layer
Ec
Ef
Ev
Ec
Ev
Ef
Ec
Ev
Ef
Ev
Ec
Energy Band Diagram and Depletion Layer
2lni
adbi
n
NN
q
kT
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EE143 – Ali Javey
Qualitative Electrostatics
Band diagram
Built in-potential
From =-dV/dx
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EE143 – Ali Javey
On the P-side of the depletion layer, = –qNa
On the N-side, = qNd
(a)
N P
Nd
Na
D eple tion La yer N e utral R egi on
–xn
0 xp
(b)
x x
p
–xn
(c)
qNd
–qNa
x
E
–xn xp
(d)
(f)
Ec
Ef
Ev
bi , built-in potential
P N
0
–xn
xp
x
bi
(e)
N eut ra l Re gion
V
s
aqNdxd
E
E
)()( 1 xxqN
CxqN
x p
s
a
s
a E
)()( n
s
d xxqN
x E
Depletion-Layer Model
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EE143 – Ali Javey
Effect of Bias on Electrostatics
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EE143 – Ali Javey
Current Flow - Qualitative
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EE143 – Ali Javey
dep
depir τ
WqnAII 0
)1(0 kTVqeII
an
n
dp
pi NL
D
NL
DAqnI 2
0
PN Diode IV Characteristics
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EE143 – Ali Javey
MOS: Metal-Oxide-Semiconductor
SiO2
metalgate
Si body
Vg
SiO2
gate
P-body
Vg
N+N+
MOS capacitor MOS transistor
MOS Capacitors
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EE143 – Ali Javey
MOS Band Diagram –
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EE143 – Ali Javey
E0 : Vacuum levelE0 – Ef : Work functionE0 – Ec : Electron affinitySi/SiO2 energy barrier
sMfbV
SiO2
=0.95 eV
9 eV
Ec, Ef
Ev
Ec
Ev
Ef
3.1 eV qs= Si + (Ec–Ef) qM Si
E0
3.1 eV
Vfb
N+ -poly-Si P-body
4.8 eV
=4.05eV
Ec
Ev
SiO2
Flat-band Condition and Flat-band Voltage
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EE143 – Ali Javey
Biasing Conditions
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EE143 – Ali Javey
Biasing Conditions (2)
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EE143 – Ali Javey
Depletion and the Depletion Width• The charge within the depletion
region is:
• Poisson’s equation reduces to:
• Integrating twice gives:
• Or:
S iO2
gate
P-Si body
+ + + + + +
- - - - - - - V
Vg > V
fb
(a)
Ec,Ef
Ev
Ec
Ef Ev
(b)
M O S
qVg
depletion
region
qs
Wde p - - - - - - - depletion layer charge, Q
de p
qVox
- - --
AqN
WxqN
dx
d
Si
A
Si
0
2
2W
qN
Si
AS
A
SSi
qNW
2
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EE143 – Ali Javey
S iO2
gate
P-Si body
+ + + + + +
- - - - - - - V
Vg > V
fb
(a)
Ec,Ef
Ev
Ec
Ef Ev
(b)
M O S
qVg
depletion
region
qs
Wde p - - - - - - - depletion layer charge, Q
de p
qVox
- - --
Surface Depletion
ox
ssasfboxsfbg C
qNVVVV
2
ox
ssa
ox
depa
ox
dep
ox
sox C
qN
C
WqN
C
Q
C
QV
2
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EE143 – Ali Javey
threshold of inversion
threshold : ns = Na
(Ec–Ef)surface= (Ef – Ev)bulk
A=B, and C = D
i
aBst n
N
q
kTln22
i
a
a
v
i
vbulkvf
gB n
N
q
kT
N
N
q
kT
n
N
q
kTEE
Eq lnlnln|)(
2
Ec ,Ef
M O S
Ev
Ef
Ei
Ec
A
B
C = q
Ev
D
qVg = qVt
st
Threshold Condition and Threshold Voltage
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EE143 – Ali Javey
oxsfbg VVVV
ox
BsaBfbt C
qNVV
222
Threshold Voltage
Bst 2
ox
stssubstfbt C
qNVV
||2
+ : N-type device, – : P-type device
Summarizing both polarities:
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EE143 – Ali Javey
• Past VT, the depletion width no longer grows
• All additional voltage results in inversion layer charge
SiO2
gate
P-Si su bstrat e
++++ ++++++
V
Vg > Vt
(a)
Ec,Ef
Ev
Ec
Ef
Ev
(b)
M O S
qVg
- - - - - ---
-
- - - - - - -
-
- - --
Qde p
Qinv
a
stsdmaxdep qN
WW2
Strong Inversion–Beyond Threshold
)( tgoxinv VVCQ
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EE143 – Ali Javey
s
2B
V f b Vt
Vg
accumulation depletion inversion
Wdep
Wdmax
Vfb Vt
Vg
accumulation dep let ion inversion
s)1/2
Wdm ax
= (2s2 qa
Review : Basic MOS Capacitor Theory
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EE143 – Ali Javey
Qdep
= q NaW
dep
0
Vfb
Vt
Vg
accumulation depletion inversion
–q Na
Wdep
Qinv
Vfb
Vt
V g
accumulation depletion inversion
slope = C ox
(a)
(b)
Qacc
Vf b
Vt
Vg
accumulation depletion inversion
(c)
– q NaW
dm ax
slope = C ox
Qs
0
Vf b
Vt
Vg
accumulation regime
depletion regime
inversion regime
Qinv
slope = Cox
total substrate charge, Qs
invdepaccs QQQQ
Review : Basic MOS Capacitor Theory
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EE143 – Ali Javey
depox CCC
111
sa
fbg
ox qN
VV
CC )(211
2
C
V f b Vt
Cox
accumulation depletion inversion
Vg
Quasi-Static CV Characteristics
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EE143 – Ali Javey
Qualitative MOSFET Operation
Depletion Layer
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EE143 – Ali Javey
Channel Length Modulation
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EE143 – Ali Javey
MOSFET I-V Characteristics – A 1st attempt
The Square Law Theory
• Current in the channel should be mainly drift-driven
• The current is:
dy
dnqnqJ nnN
dy
dQZ
dxyxndy
dqZ
dzdxJI
Nn
yx
n
NyD
c
)(
0
),(
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EE143 – Ali Javey
MOSFET I-V Characteristics – A 1st attempt• But, current is constant through the channel:
• We know the inversion layer charge:
• Accounting for the non-uniformity:
D
D
V
NnD
V
NnD
L
D
dQL
ZI
dQZLIdyI
0
00
)( TGoxinv VVCQ
)()( TGoxinv VVCyQ
TG
DsatDDDTGoxnD VV
VVVVVVC
L
ZI
0
2
2
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EE143 – Ali Javey
MOSFET I-V Characteristics – A 1st attempt• Past pinch-off, the drain current is constant
• So:
• Now, in the pinched-off region:
DsatVVDVVD IIIDsatDDsatD
,,
TGDsat
DsatTGoxinv
VVV
VVVCyQ
0)()(
2
2Dsat
DsatTGoxnD
VVVVC
L
ZI
22 TGoxnD VVC
L
ZI
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EE143 – Ali Javey
N-channel MOSFET
Layout (Top View)
4 lithography steps are required: 1. active area 2. gate electrode 3. contacts 4. metal interconnects
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EE143 – Ali Javey
1) Thermal oxidation (~10 nm “pad oxide”)
2) Silicon-nitride (Si3N4) deposition by CVD (~40nm)
3) Active-area definition (lithography & etch)
4) Boron ion implantation (“channel stop” implant)
Simple NMOS Process Flow
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EE143 – Ali Javey
5) Thermal oxidation to grow oxide in “field regions”
6) Si3N4 & pad oxide removal
7) Thermal oxidation (“gate oxide”)
8) Poly-Si deposition by CVD
9) Poly-Si gate-electrode patterning (litho. & etch)
10) P or As ion implantation to form n+ source and drain regions
Top view of masks
Simple NMOS Process Flow
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EE143 – Ali Javey
11) SiO2 CVD
12) Contact definition (litho. & etch)
13) Al deposition by sputtering
14) Al patterning by litho. & etch to form interconnects
Top view of masks
Simple NMOS Process Flow